Tsum Tsum "My Way or the Highway"?

Nope.  You can play the game any way you want.  No obligation, just send a few hearts my way every so often and we're good.

That said, you can make it easy for others by following three simple rules about playing Tsum Tsum.

1. Avoid "Claim All" and use "Check" to claim every heart, even if the 1 hour has expired. Note that its perfectly ok to do a claim all to clear out an excessive number of hearts.  Just be aware that none of the hearts sent to you have been returned to the senders, and any hearts sent by unknowns can't be returned using "Claim All"
2. Turn on notifications in Line and in Tsum Tsum.  This lets others see the number of heart's and chat group messages you're sending.  I have mine turned on, but keep the sound off. You may not want to do this on your phone and that's ok.
3. To remove people from your list, use hide and remove.  Never block except if someone is behaving in an offensive way*.  I think offensive behaviour is extremely rare in Tsum Tsum.

Here's what I do when playing:

First, I check every heart I've received
Next, I send to everyone on my list.
I check in with the groups I'm in just to say hi if nothing else
Sometimes I actually play the game.
Notifications are always on on at least one device.

If you're not getting a LOT of hearts from me, check in with one of the groups I'm in and send me a message if I appear to be active.  Maybe you're not on my list for some reason and need to be added or unblocked.  Just ask.  I'll be happy to oblige.

*Note that I used to block people who I thought were not sending back hearts.  In some cases they weren't, but in others, I just missed them because they had notifications off.  Blocking may make it difficult to get someone back on your list and should only be used for individuals behaving badly.  Not sending hearts is not bad behaviour.  Use Hide and Remove instead.